Floodgate

You can breathe a sigh of relief. You've faced a number of challenging missions thus far, and at last you've come to one that doesn't require nearly as much effort. The mission title suggests something rather horrific, but in actuality, the Flood is far easier to deal with in Halo 3 than in any previous Halo game.
You'll be going up against some of the usual suspects including Infection Flood, Carriers, and both Human and Elite Combat Flood. Added to the mix are characters such Brute Combat Forms (which are a joke at close range) and the new Pure Forms which you'll be dealing with near the end of the mission.
Get ready to run like a mo-fo!

It Followed Me Home

Poor Chief just can't catch a break can he? You'll be starting out exactly where the previous mission left off. Only now the sun is setting on a Flood-infested Voi, and you'll be backtracking through the mess. You start with an assault rifle and battle rifle.
As you follow the hillside down towards the town, keep the BR and lose the AR. When you reach the buildings and take your first left, you'll notice a dead Chieftain with a Gravity Hammer laying next to him. Since he's not using it anymore, switch out your AR for it and proceed onward. Keep to the right side as you approach the clearing. You'll hear the Marines scream as waves of Flood start pouring down from the rooftops. Survive by following the path in the video below.

Make your way past the ammo crates and through the door. Finally! We get to watch the Flood feed and transform humans into Combat forms! Well, at least if you choose to. I tend to show a little mercy and hammer the poor bastard to death. Move straight through the next area and ignore the Flood. They'll be too busy fighting the Marines to pay any attention to you. Head through the Traxus opening, hang a left, bolt through the next opening, turn right, and run through the next area too. Continue to ignore the Flood as you jump on the crates to gain access to the catwalk. Now just follow the path to the "white room" on the far side and drop down through the hole.
As soon as Cortana finishes talking, arm yourself with the hammer and proceed through the doors.

As you turn the corner, you'll run smack-dab into a group of both Human and Brute Combat Flood. Swing away, Meryl! A few swings should smash them to pieces. Notice how easily they crumble from the melee of a weapon. While other weapons won't cause the same splash damage as the gravity hammer, they'll still split apart the Flood's weak bodies unlike in previous games. As an added bonus, you'll be recharging your shields with every melee. This one little detail tends to make Flood-based levels simpler than ones containing the Covenant.
Head through the door and you'll hear the frightened wails of a petrified Marine who just watched all of his buddies meet a bitter end. This brings back haunting memories of the insane Marine back in the original game. Good times!
Exit the door and head back into the second lakebed from the previous mission. You'll trigger a cut scene...

Shadow of Intent

The Elites finally make their grand entrance! It only took them half the game to show up...
Your Elites won't last long in this area, but while they live, these guys are grenade-throwing machines! Don't get in their way. Let the Flood deal with them. Remember how reckless your Marines were with frags in the last level? Well imagine that kind of carnage with plasma grenades.

Hang out on the catwalk for now and enjoy the spectacular view of the wide-open portal pouring wisps of blue energy into the sky. When additional Combat Flood begin leaping forth from the crater, caused by the crashed Covenant cruiser, switch over to your battle rifle and begin headshotting them one by one.
Headshotting Flood has never been possible until now, but their new design reveals a single Infection Flood sticking out of the chest of the body it has taken over. Shooting it with a weapon such as a battle rifle or carbine counts as a headshot, and the Combat Flood will drop. Note that if the body is still intact, another Infection form can bring it back to life by entering its chest cavity.
Multiple waves of Flood will emerge from the crater. Just take them on one group at a time. Eventually two Carriers will start waddling down the ramp on the far side. Once you've cleared the area of Combat Flood, head down and use plasma grenades to stick the Carriers. The explosion will kill both the Carrier and the potential Infection forms.

Trade out your hammer for an Energy Sword for the first time in the campaign, grab the bubble shield from a little further back if you haven't already (save it for later!), and head up the ramp into the building. Just beyond the truck, a large mass of Combat forms awaits your arrival. Switch to your battle rifle and take them out one at a time. Arbiter does a pretty decent job lending a helping hand. If they get too close, whip out that energy blade and turn them into sushi. The only real strategy here is dealing with them in moderation.
When the fist group is down, walk towards the other side of the room to trigger the second wave. Again, deal with them just like you did the previous group. Now head up the stairs and into the next area where the War Chieftain was in The Storm. Groups of Combat forms will begin spawning. Killing them now will save you the trouble of having to face them when they attack from behind.
At last we reach the final run. Not bad so far, right? Things are about to get a little zesty. Looking outside you should see something new and big. Meet your new nemesis, the Flood Pure Form. What makes them unique? Apparently made from bones of infected bodies, Pure Forms have the ability to mutate at any given time into three distinct forms. The most common for is the Stalker. Its attack abilities are limited to a short, non-lethal lunge, but it also has the ability to scale just about any vertical surface like a spider. Tank Flood, on the other hand, are near invincible to every type of offensive measure except for flame weapons and the energy sword. They can't harm you from a distance, but these hulking masses of flesh have a one-hit-kill melee that'll send you flying if you get to careless. Last we have the Ranged Flood. They highly resemble Venus Flytraps and cling to walls as they shoot unlimited rounds of carbine-like projectiles in your direction. These are by far the most dangerous and the most annoying Pure Forms out there.
Moving on, you'll hear Johnson mention they think Cortana is trapped inside the crashed ship. Hurray!

You're about to witness the full might of a Tank form. Watch as two green ally Phantoms drop off a whole platoon of Elites, surround the Tank Flood in the center of the platform, and continuously grenade spam him to no effect. The Tank form will eventually move in and slaughter his foes. While he does, skip along the right edge and use the Traxus crates for cover. If anything gets in your way, attack it with the energy sword, like with the hammer, this doubles as a source for shields.

Infinite Devil Machine

When you reach the crashed Flood ship, hug the right hand side and move along carefully. A handful of Pure forms in various states will be guarding the entrance into the vessel. As soon as the Ranged Flood start shooting, drop the bubble shield and head up the slop towards the opening. If you're having trouble running through this particular segment, please see the "Exterminator" video I've provided in my file share. A fileshare link has been provided at the top of the page, or a video link just below (no voice-over). This illustrates how to wipe out all potential threats in the area.

Once you drop inside, maneuver your way through the Flood-flesh-covered corridors (a rather grim scene of things to come) and into a larger room where "Cortana" will be waiting on the other side. Retrieve her to end the level and to trigger the longest cut scene in the game... only to find out it wasn't really her after all...